Spatial/Temporal Patterns in Weddell Gyre Characteristics and Their Relationship to Global Climate

Transcription

1 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 1 Spatial/Temporal Patterns in Weddell Gyre Characteristics and Their Relationship to Global Climate Douglas G. Martinson 1,2 and Richard A. Iannuzzi 1 Lamont-Doherty Earth Observatory Palisades, NY, Department of Earth and Environmental Sciences Columbia University New York, NY Abstract. We examine the spatiotemporal variability of the upper ocean-sea ice system of the Atlantic sector of the Southern Ocean subpolar seas (Weddell gyre), and the nature of its covariability with extrapolar climate, identifying teleconnections and their mechanisms. To systematically evaluate the sporadic and sparse distribution of subpolar data we employed an optimal analysis involving Empirical Orthogonal Functions (EOFs). The EOFs reveal that the spatial pattern of coherent spatial covariability of Weddell gyre characteristics is dominated by high interannual variability near the northern (circumpolar) rim of the gyre and lesser variability (10-20% of the variance) in the gyre's central core region. We find considerable, statistically-significant teleconnections between subpolar and extrapolar climate. The dominant link is with ENSO over its broad region of influence, whereby the subpolar upper ocean response is enhanced winter-average cyclonic forcing during tropical warm events (El Niño); the opposite occurs for cold events (La Niña). During El Niño the subpolar gyre contracts so the pycnocline shallows in the gyre center and deepens at the northern rim; sea ice expands northward leading to enhanced surface freshwater in the northern rim. This regional subpolar response is consistent with recent GCM modeling analyses showing that equatorial warm anomalies trigger an increase in the Pacific equator-pole meridional temperature gradient which shifts the subtropical jet equatorward, and farther from the available potential energy of the Antarctic, decreasing the cyclone activity and climatological forcing of the Pacific subpolar gyres. The Pacific equatorial warming also perturbs the Walker cell circulation leading to the opposite response in the Atlantic, resulting in increased cyclonic forcing in the Atlantic's subpolar gyre. We also find that the Weddell gyre interior OAI characteristics covary with sea ice extent in the Atlantic region, and inversely with the sea ice extent in the Amundsen/Bellingshausen regions, reflecting a strong Antarctic Dipole. 1. Introduction Hypotheses, models and observations suggest that the polar oceans play an important role in global climate through a multitude of polar-unique processes operating over a variety of time scales [e.g., Walker, 1923; Fletcher, 1969; Kellogg, 1975; Walsh, 1983; Chiu, 1983; van Loon, 1984; Simmonds and Dix, 1986; Mitchell and Hills, 1986, James, 1988; Large and van Loon, 1989; Trenberth et al., 1990; Simmonds and Wu, 1993; Rind et al., 1995; Krishnamurti et al., 1986; Imbrie et al., 1992]. Numerous studies have considered the local/regional interactions between the sea ice and underlying ocean Lamont-Doherty Earth Observatory Palisades, NY, Department of Earth and Environmental Sciences Columbia University New York, NY [e.g., Gordon, 1981; Gordon and Huber, 1984, 1990; Lemke, 1987; Martinson, 1990], while others have investigated the spatial/temporal distribution of the largest scale teleconnections and mechanisms capable of explaining them at that scale [e.g., Chiu, 1983; van Loon, 1984; Krishnamurti et al. 1986; James, 1988; Karoly, 1989; Meehl, 1991; Simmonds and Law, 1995; White et al., 1998; Peterson and White, 1998; Hines and Bromwich, 1999; Yuan and Martinson, 2000a]. Regardless, our documentation and understanding of the detailed nature of the polar-extrapolar teleconnections, and their underlying causal and mechanistic links across the full range of scales (local, regional and global), are still quite rudimentary. The purpose of this paper is to further document and improve our understanding of the manner by which the polar-extrapolar teleconnections are communicated across the hierarchy of scales involved.

2 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 2 2. Approach Our strategy for documenting and understanding the relationship between variability in the ocean-atmosphereice (OAI) system and extrapolar climate, and their linkages across scales, requires the following: (1) quantify the local and regional temporal/spatial variability of climatically-meaningful characteristics of the OAI system (we do so for one of the predominant Antarctic subpolar gyres: the Weddell gyre), (2) correlate the time series of these OAI characteristics to those of extrapolar climate variables and indices, and evaluate the correlation statistics, (3) identify those OAI characteristics that show the most robust links to extrapolar climate and determine the underlying local physical changes responsible for their variability, and (4) evaluate mechanisms consistent with the polar-extrapolar links and observed local OAI changes. This paper develops the methodology and focuses on two primary OAI characteristics, while a companion paper (in preparation) presents the full suite of OAI characteristics and their extrapolar covariability. 2.1 Climate Variables OAI System Parameters. We adopt the climatically-meaningful OAI characteristics as quantified through the bulk property parameters of Martinson and Iannuzzi [1998; hereafter MI98]. MI98 focus on robust and relatively long-lived information contained within the upper ocean structure. Specifically, vertical integration of temperature (T) and salinity (S) profiles provide bulk property distributions which are used directly, or in combinations, to provide fundamental OAI information on ocean ventilation, water column stability and sea ice growth constraints. The OAI parameters are dominated by two bulk properties: (1) a "thermal barrier" (TB w ), which is the enthalpy relative to the freezing point available within the permanent thermocline; and (2) a "salt deficit" (SD w ), which is the freshwater surplus in the winter surface layer relative to the deep water (in terms of buoyancy, allowing for the nonlinear equation of state, vertical salt flux, etc.; see MI98 for details). SD w must be eliminated by salt input in order to destabilize the surface layer and drive catastrophic overturn. TB w is the sensible heat that must be vented during erosion of the pycnocline, accompanying elimination of SD w. As it is vented, this heat stabilizes the water column by melting ice or, equivalently, by preventing ice growth which would otherwise destabilize through salt rejection. Over seasonal time scales, SD w is reduced by salinization during ice growth, initiating static instability that drives an entrainment heat flux venting TB w, and freshening and restabilizing (to some degree) the surface layer through ice melt. TB w thus provides a negative feedback to the ice growth-driven destabilization process. For practical purposes SD w and TB w are normalized into equivalent units of effective ice thickness per unit area. As such, SD w reveals the thickness of in situ ice growth required to reject enough salt to destabilize the surface layer; TB w reveals the thickness of ice that could be melted by completely venting the thermocline, and it indicates the potential to resist overturn due to the heat storage in the thermocline (i.e., delivered by circumpolar deepwater, CDW). In various combinations TB w and SD w provide the basis for additional parameters of interest. Here we focus on two climatically-relevant parameters: (1) bulk stability, Σ = TB w +SD w, and (2) total ocean heat flux, F T. Bulk stability is the maximum amount of in situ ice growth, or latent heat loss, that the upper ocean can support before destabilizing the water column, flipping the system to its unstable (thermal) mode of Gordon, 1991, and generating open ocean deep water formation and preventing winter ice growth, Martinson [1990]. Essentially, Σ provides an indication of the total amount of surface buoyancy stabilizing the surface water column and allowing sea ice to form at all. It places an upper limit on in situ ice growth. Total ocean heat flux, F T, is the sum of turbulent diffusive (F D ) and entrainment (F E ) heat fluxes entering the surface ocean mixed layer across its base. These heat flux components are determined as follows. The external forcing for winter ice growth, F L, is the upward flux of heat at the bottom of the atmosphere, F a, less the upward flux of oceanic sensible heat into the mixed layer created by turbulent diffusion; so F L = F a - F D. Seasonallyaveraged values (indicated by <>) of these fluxes dictate the entrainment heat flux <F E > occurring when surface convection, driven by F L induced ice growth salinization forces entrainment into the mixed layer of warm underlying pycnocline waters. Specifically, <F E > = <F L >TB w /Σ. TB w /Σ indicates what fraction of the initial latent heat of fusion is converted, by the negative feedback, into sensible heat. The diffusive heat flux <F D > is parameterized as proportional to the thermal gradient ( T) through the thermocline, so <F D > = <k T >ρc p T, where T is the depth-averaged T through the thermocline, ρ is the density of seawater ( kg/m 3 ), and c p its heat capacity (4.18x10 3 J/ Ckg). The seasonally-averaged winter turbulent diffusivity coefficient, <k T >, across the pycnocline is rather large in the Antarctic (see MI98), 0.66x10-4 m 2 /s, reflecting small values during quiescent periods averaged with substantially increased values

3 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 3 during frequent intense polar lows [Stanton, personal communication]. The total ocean sensible heat flux is <F T > = <F E > + <F D >. <F T > estimated in this manner shows excellent agreement to the seasonally measured value of McPhee et al., [1999]. Additional insights regarding the nature of the ocean-ice interaction are provided by other combinations of SD w and TB w. These are described and their variability evaluated in the companion paper. For geometrically ideal T and S profiles, TB w and SD w are computed from simple algebraic relationships. These show that the parameters are functions of the following physical characteristics (external system parameters) of the upper water column: S ml, z ml, T pp, S pp, z pp (heat fluxes also depend on k T, F L ); z indicates a depth, and subscripts indicate the quantity's value within the mixed layer (ml) or at the base of the permanent pycnocline (pp). These algebraic expressions allow us to quantify the degree to which individual external parameters are controlling variability observed in the climatically-meaningful bulk parameters. This defines their sensitivity and allows us to relate local water column changes to regional or global scale forcings (helping identify and/or constrain plausible mechanistic links). MI98 provide 25-year climatologies for each of the bulk property parameters within the Weddell gyre region (polar gyre from the Antarctic Peninsula to approximately 20 E, spanning the Weddell-Enderby Basin). They are based on historical CTD data from 28 cruises, involving 1423 hydrographic stations (of 1710) that survived considerable quality control and error analysis. The spatial variability in the climatologies have a spatial signal to noise ratio (S/N) of 20 db. Here we determine the variability (detrended yearly anomalies) about these climatological means, as a function of year and location within the gyre, focusing on Σ and <F T >. These anomalies provide the means for comparing the temporal and spatial variability of the OIA interactions in the interior of the polar gyres to that of extrapolar climate variables and indices. 2.2 Extrapolar Climate. Extrapolar climate variability is measured through a wide variety of existing variables and indices. Yuan and Martinson [2000a; hereafter YM00] examined the relationship between 20-year records of detrended anomalies in the Antarctic monthly sea ice edge position (SIE * ) and: (1) detrended surface air temperature (SAT * ) at 5 x5 intervals throughout the globe based on National Center for Environmental Forecast (NCEP) and National Center for Atmospheric Research (NCAR) reanalysis surface air temperature at the 1000 Mb pressure level [Kalnay et al., 1996]), (2) SIE * in 12 contiguous longitude bands (representing the lateral SIE * decorrelation length) around Antarctica, and (3) largescale climate indices such as NINO3 (an ENSO-related index based on eastern equatorial Pacific sea surface temperature, SST, averaged in 5 N to 5 S and 150 W to 90 W and robust index for ENSO variability; Cane et al., 1986), the Pacific-North America teleconnection index (PNA), North Atlantic Oscillation index (NAO), and Southern Oscillation Index (SOI), as well as several other indices. YM00 found considerable, statisticallysignificant global, circumpolar and index correlations almost twice as many strong global correlations (teleconnections) as would be expected by correlating noise time series with similar spectral coloring and quasi-periodic components as displayed in the actual SIE * records. YM00 performed extensive statistical analysis of the correlations between SIE * and extrapolar climate, assessing the robustness and likelihood of the links between extrapolar climate and variability in the circumpolar belt around Antarctica. Hoping to draw on that statistical foundation, we use the same climate variables and indices in this study, as well as SIE *. The latter allows us to determine the extent to which the OAI interactions within the interior of the polar gyre are related to that of the circumpolar margins, as indicated by the ice extent anomalies around the gyre rim. 3. Methods Several studies [e.g., van Loon and Shea, 1985; Carleton, 1988; Gloersen, 1995; Ledley and Huang, 1997; YM00; Simmonds and Jacka, 1995; Stammerjohn and Smith, 1997] have demonstrated a relationship between the subpolar seas and ENSO; perhaps not surprising given the global spatial influence of ENSO [e.g., Ropelewski and Halpert, 1987]. Thus, to test the feasibility of our approach, we begin by examining the relationship between ENSO and bulk stability (Σ) and ocean heat flux (<F T >) as computed near the center of the Weddell gyre where the observations are most dense. As seen in Figure 1, Σ and <F T >, averaged annually within a spatial domain encompassing Maud Rise, from S and 20 W - 8 E. For years in which data exist, the OIA parameters appear to be well correlated with ENSO (r = 0.95 and for Σ and <F T >, respectively; significant at the 99.98% and 95% confidence levels (see Appendix for discussion of bootstrap method used to determine significance). The correlations are highly significant, even despite the relatively few data points and sparse, irregular distribution. Note that despite the apparently large scatter of <F T > in Figure 1 relative to that of Σ, <F T > has a

4 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 4 Figure 1. Solid line is NINO3 index of ENSO phenomenon; circles are bulk stability (Σ) from central Weddell gyre region (yearly averages from within 20 W - 8 E and S spatial domain); crosses are total winter average ocean heat flux (<F T >) from the same region as Σ. Ordinate for all three time series is given on left of figure in z-scores (standard deviations from mean values). Error bars on Σ and <F T > points reflect scatter within spatial domain. r Σ gives the degree of linear correlation between NINO3 and Σ and r <FT between NINO3 and > <F T >. Confidence level of correlations (presented symbol) are determined from bootstrap PDF (inset). Instantaneous correlations (r'; see Appendix for details) given as function of abscissa by boxes at lower portion of figure show percent contribution of each pair of points to overall correlation (solid r' for bulk stability; dashed r' for <F T >). coefficient of variation (ratio of standard deviation to mean), of 0.36, so the scatter in <F T > is still reasonably small relative to the domain's mean <F T > value. The instantaneous correlation (r'; see Appendix for description), shown in the lower portion of the plot in Figure 1, reveals that the strong correlations are dominated by the fact that the OAI parameters covary most strongly during the extreme ENSO events of 1984 and 1989 the close correspondence during these years overwhelmingly accounts for the high degree of correlation. Unfortunately, we do not have long enough records to determine if this indicates that the correlation (assuming it to be causal) reflects a mechanism that is only operative when extreme events occur, or whether the mechanism is operative all the time, but dominated by the large variance events as dictated by the construction of a correlation coefficient. Results of Figure 1 suggest that El Niño years are accompanied by

5 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 5 anomalously strong bulk stability and low ocean heat flux, and vice versa in La Niña years. This negative covariation works to offset their local OAI impact (see Section 5 for more discussion). The covarying relationships found here are tantalizing enough to warrant more rigorous investigation. Unfortunately, elsewhere in the Weddell gyre the data are too sparse and sporadic, with low S/N, to extend this analysis. Furthermore, the short length of the time series make their actual and long-term physical significance questionable (though their true statistical significance for their length is well determined by the bootstrap method employed above). In order to facilitate further analyses and enhance S/N, we interpolate the data of the Weddell gyre region onto a grid that allows direct application of standard analysis tools, including characterization of the spatial/temporal patterns through EOF analysis. Since interpolation may introduce methodological errors into our findings we further investigate results arising from the gridded (interpolated) data by repeating the relevant analysis using the uninterpolated data, and examining (to the extent possible) the degree to which the primary correlations and patterns are preserved. In this manner we eliminate correlation attributed to the interpolation process itself, but still gain the benefits of working with evenly sampled series. 3.1 Optimal Analysis We use the reduced space optimal analysis (OA) scheme of Kaplan et al. [1998; hereafter, KKCB98] to produce a smoothly interpolated data set that best preserves the coherent spatial/temporal structure already inherent in the data. The OA method involves the following steps (see KKCB98 for complete details): (1) define a grid consistent with the gyre dynamics and data distribution; (2) estimate average bulk property values in each grid cell for each year; (3) estimate the sample covariance matrix (C^ ; hereafter referred to as the covariance matrix, ignoring the "sample" qualifier) for the series in the grid (i.e., quantify how the data covary in space and time across the sampled domain); (4) compute the empirical orthogonal function (EOF) structure from the covariance matrix, representing a physically-consistent basis for the observations, where the lower order EOFs represent spatially-coherent structures whose shapes are preserved through time; (5) reduce the space (increasing S/N) by throwing away those EOFs that represent uncorrelated noise, spatiallylocalized signal or describe little total variance; (6) combine the surviving (dominant) EOFs to provide a smooth, reduced-space interpolant for the data across the grid in space and time; and (7) interpolate the data using an objective function that optimizes the fit of the preserved EOFs to the data for each year, while preserving a low-order time-varying component described by an autoregressive (AR) order one process (a Markov process). The objective function of the last step assures that the interpolation not only provides the best optimal fit of the EOFs in space at any one time, but that it also avoids any abrupt (presumably unnatural) temporal shifts in the EOF amplitude from one year to the next. Once the data have been interpolated, so as to provide a densely-populated data matrix (except for years in which data does not exist anywhere across the grid: 1979, 1980, 1982, 1987, 1988, 1991 in our 25 year period), the covariance of this matrix is decomposed to provide the full modal structure of EOFs with their timevarying amplitudes indicated by their principal components, PCs. Years for which no data exist are further interpolated by fitting the PCs using both linear and cubic spline interpolants (we evaluate the sensitivity of all correlation results according to which interpolant, linear or spline, is used to fill gaps in the PCs results suggest negligible sensitivity to this). The optimal analysis provides an ideal internallyconsistent means of utilizing sparse historical data, but it is sensitive to a number of factors. One factor is the uncertainty in the original data. This uncertainty reflects a combination of the scatter in individual estimates of the bulk parameters lying within any one grid cell for a given year, as well as the individual precision in each estimate reflecting the uncertainties propagated through analysis of an individual profile (both uncertainties are accounted for in the averaging process). This uncertainty is quantitatively tracked through the OA process, as it defines an error matrix. More subtle is the sensitivity to the actual grid chosen, as well as to the construction and normalization of the dispersion matrix used to determine the EOF basis for the interpolant. For example, use of a correlation matrix instead of covariance matrix emphasizes covarying structure independent of absolute amplitudes; important if we expect that some region of the gyre may naturally display larger amplitude variability than other regions. In addition, the manner in which the statistical moments are estimated for the covariance matrix elements (e.g., normalizing to a full domain mean, versus grid-specific means) influence the resulting EOFs and the interpolation. Sensitivity to these constructs are investigated Gridded Data. The grid structure for the Weddell gyre spatial domain must be consistent with the gyre dynamics and the general spatial structure of the upper ocean property distributions. This assures that averaging quantities

6 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 6 within individual grid cells makes physical sense. In order to develop the grid we examined individual cruise tracks, as well as the climatologies of MI98 in an effort to locate fronts, abrupt property transitions and regions of maximum lateral property gradients; where properties varied more smoothly, we determined spatial decorrelation lengths. The former reveal natural grid cell boundaries and, in their absence, the latter constrains grid cell size. The latter also helps define length scales required to avoid EOF aliasing [North et al., 1982]. This analysis suggests a physically-optimal configuration as shown in Figure 2. Unfortunately, the physically-optimal grid includes cells for which insufficient data exist to provide robust estimates of the parameters and a stable covariance matrix. To alleviate the problem we combined grid cells until we achieved a grid distribution (Figure 2, combined cells are revealed by common cell number) that consists of 16 spatial grid cells which preserves, to the extent possible, the natural property boundaries of the optimal grid and is compatible with the data density. The latter is satisfied by obtaining a stable covariance matrix as defined by the fraction of negative eigenvalues in the EOF decomposition (negative values reveal a violation of the positive semi-definite criterion and reveals an internally-inconsistent estimate of the covariance matrix). We compute the various OAI parameters and local physical characteristics using 1423 CTD upper ocean profiles (see Figure 2 for station locations, independent of time), existing from 1972 to the present. Outliers in individual parameter estimates are identified as lying three or more standard deviations from that year's mean value in any particular grid cell; they are eliminated prior to averaging and constitute ~5% of the total data. We then average all remaining values that lie within a grid cell existing for each year. This provides us with "superdata": averaged values for different grid cells and different years. The super-data for each parameter occupy a sparse data matrix, T o ; only those cells for years in which data exist within the cell are occupied. The error, as a standard deviation of each super-datum value, is determined during the averaging process; cells 1 and 2 in the grid are poorly sampled Covariance Matrix and EOF Decomposition. Given the reference grid, covariance matrices, C^, were estimated for each super-data matrix, T o (one matrix for each parameter evaluated) Covariances involve standardization to local temporal means and standard deviations of the quantity within each particular grid cell. They are estimated by computing biased (because of the limited data) covariance between time series from all pairs of grid cells, involving mutually occupied years only. As suggested by KKCB98, application of a spatial filter to the data, or comparably, to the covariance matrix directly (to bypass problems associated with data gaps present in the original data) stabilizes C^ when constructed in data-poor regions, as is the case here. However, we find this filtering to artificially alter the nature of the covariance too much. It also adds considerable sensitivity to the PCs, though the EOF spatial structures are little influenced. As the analysis is critically dependent upon the PCs we do not perform any filtering of the covariance matrix in our analysis. Once the covariance matrix is estimated, its Figure 2. Grid scheme for the optimal analysis of the historical data of the Weddell gyre spatial domain. Individual grid cells reflect ideal physically-consistent grid. Cells sharing same grid-cell number have been merged into singe cells to produce the most stable physically-consistent grid (used for the primary analysis in the paper). Station data used in analysis are indicated by light dots.

7 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 7 eigenvector structure is computed to obtain the EOFs. We examine scree plots to determine the EOF noise floor and preserve, for the interpolant, all EOFs lying above the noise floor, typically the 3 leading EOFs. In most cases, the first 1-3 EOFs describe the vast majority of the total variance (recognizing the caution of North et al., 1982, these leading EOFs do not contain or split pseudodegenerate multiplet sets). Once the EOFs are determined, we can use those that are preserved as a reduced-space interpolant basis, apply the objective function to interpolate the super-data, producing a smoothed, gridded data matrix, T^. From the covariance matrix of T^ we compute the full set of EOFs and their PCs. As expected, the lowest order EOFs are nearly identical to those originally used in the interpolation, but now, with the full matrix we can recover their temporally-varying expansion coefficients in the PCs and the complete internally-consistent modal structure for the observations. 3.2 Uncertainties Super-Data Uncertainties. We estimate uncertainties in the bulk parameters used in the super-data as described fully in MI98. These provide an estimate of how noise in the individual realizations of T and S profiles manifests itself as uncertainties in the specific bulk parameter values Interpolation Error. Several errors are investigated regarding the interpolation. The most fundamental error is the synthesis error, or interpolation precision, σ s, reflecting the smooth fit of the reduced-space interpolant. It is given as: σ s = Var[T^-T o ] 1/2 (where Var[X] = E[(X- E[X])(X-E[X]) T ]) for the mutually populated cells only in other words, how well does the interpolant fit the super-data in each grid cell (illustrated by vertical discrepancies between the circles and bold crosses in Figure 3), averaged over the different years. More important is the interpolation accuracy, σ a ; that is, with what fidelity does the interpolant fill gaps. We estimate interpolation accuracy (KKCB98's truncation error) by eliminating a single super-datum point, and repeating the interpolation process (illustrated by vertical discrepancies between the bold crosses and x's in Figure 3). From this, we evaluate ε a,i = (T^-T o ) n,m where n, m indicate the error evaluated at the eliminated superdatum element only. We repeat this process, each time eliminating a different datum after replacing the previously eliminated datum (the data are not dense enough to afford the luxury of withholding a significant portion of the data from the original interpolation). After this has been done for each super-datum point, the full suite of ε a values are evaluated for the average rms accuracy error between the interpolated value at the Figure 3. Standardized Σ time series for grid cells 6 (lower curve) and 11 (upper curve); see Figure 2 for cell locations. Bold crosses show original averaged values in cell (superdata values); circles connected by dashed lines show reduced space interpolation involving 3 leading EOFs (not exact fit to super-data because of space reduction); bold x's indicate interpolated values when the super-datum at that time was eliminated from the data base prior to the OA interpolation, thus it gives an indication of how well interpolant can fill temporal gaps in data base. missing datum and the true (eliminated) values as σ a = Var[ε] 1/2. Treating bulk stability as representative, we find that σ s = 0.68, while σ a = This suggests that the accuracy is just better than twice the precision in other words, the interpolated values in regions missing data are, on average, likely to lie within two standard deviations of the scatter (precision) of the data throughout the domain. As might be expected, the accuracy error shows spatial variability, reflecting the fact that gaps are filled better in regions that show strong covariability to neighboring cells across the domain, or in regions of denser surrounding data. Figure 3 gives results from two grid cells: one (cell 11) is densely sampled, the other (cell 6) is sparsely sampled. Uncertainties associated with the sensitivity of the method to the nature of the covariance matrix, grid definition and normalization constants are assessed via sensitivity experiments. Specifically, we repeated the analysis using different grid schemes (including: zonal, meridional, and higher density), and different normalization schemes (including: a full-domain spatial mean, correlation versus covariance). Results of these

8 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 8 different experiments suggest to us that the results presented in the next section are fairly robust with respect to the interpolant. More importantly, the changes obtained in EOF patterns did not alter the relative spatial distribution of variability across the domain. However, we estimate a more significant sensitivity in the PCs. Fortunately, the implications of this last number are largely circumvented since we use the PC correlations with extrapolar climate variables/indices to guide further investigation with the non-interpolated data (super-data), as mentioned previously. Most importantly, as an exploratory device, the sensitivities in the results did not suggest any alternate investigations with the noninterpolated data, other than those suggested in the primary analysis. Finally, the nature of the EOF basis depends on the quality of the covariance matrix we estimate for the data across the grid. Ideally, C^ is estimated directly from the quadratic operation on the grid's fully-populated data matrix, T o. Instead, our data are insufficient for this so we must estimate C^ directly. This allows admittance of inconsistent structure (violation of the positive semidefiniteness). Therefore, the presence of negative eigenvalues reveals inconsistencies in our estimates of how different series across the grid covary. We determine where such inconsistency arises, thus identifying which grid cells are yielding the poorest estimates of covariance, and reducing the overall quality of our EOF decomposition and external correlations. We do this by repeatedly subjecting individual values within a correlation matrix to random perturbations and assessing their probabilistic influence on the degree of negativity in the eigenvalues. We work with a correlation matrix in this case to constrain the magnitude of the random perturbations, but given the relatively small spatial domain, the EOF structure is little altered from that obtained from the covariance matrix. From this we identify those cells with the biggest impact, and thus representing the most poorly estimated series. This helps guide future sampling strategies, identifying those grid locations requiring additional information to reduce the uncertainties they introduce in the analysis. Somewhat surprisingly, we found that the error is more or less evenly distributed across all of the grid cells; perturbations in no one grid cell displayed a significantly larger influence than perturbations in any other grid cell. 4. Results Our analysis findings are presented as follows: (1) results of the regional space/time variability as revealed by the EOF patterns and their PCs; (2) the covariability of these EOF patterns with indices and variables of extrapolar climate variability (teleconnections); (3) determination of the local/regional physical variables controlling the variations in the teleconnected characteristics. The consistency of the gridded data results at the various stages are evaluated through use of the uninterpolated super-data. These results are followed by a discussion of potential mechanisms explaining the observations over the variety of scales considered. 4.1 Gridded Data Analysis Spatial/Temporal Variability. Three leading EOFs lie above the noise floor for both Σ and <F T >. These EOFs and their PCs, describing 43%, 20% and 9% of the total variance for Σ and 31%, 25% and 18% for <F T >, are presented in Figure 4. The spatial distribution of the variance described by each EOF is determined by correlating the mode's PC to each cell in the gridded data (T^). The fraction of variance explained for each grid cell is proportional to the EOF peak amplitude of that cell. Correlating the PC to the original super-data (T o ), to the extent allowed by the super-data distribution, reveals similar r 2 spatial structure though poorer definition given the sparse data. However, in this latter case the southwest region of the gyre shows little explained variance, contrary to the case for the second and third modes of the gridded field. This suggests that the OA is imposing more coherent structure in the SW than actually exists in the data likely a consequence of the particularly poor data density in that region of the grid. Consequently, we treat results arising from the gridded data in the SW region with considerable skepticism, and look to additional future data to help better constrain this portion of the domain. The first two modes of both Σ and <F T > show similar spatial patterns and are clearly dominated by variability concentrated in the northern extent of the gyre. The EOF spatial structures (of coherent interannual variability) do not mimic the climatological patterns shown in MI98, though the latter does show considerable bulk property gradients through the northern rim of the gyre where it encroaches upon the subtropical regions. There is a reversed polarity between bulk stability's first EOF's amplitude in the NE and NW regions, while a comparable pattern in the first EOF of <F T > does not show the reversed polarity. The second mode EOFs, for both Σ and <F T > introduce a shorter wavelength fluctuation in the same northern region, though they also pick up the southwest (this latter influence presumably a consequence of the interpolation as stated above). Note that neither of the first 2 modes for either parameter describes much variability within the eastern core of the gyre, though even in the central western core of the gyre, the low amplitude of the first

9 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 9 Figure 4. Lowest order modes, EOFs and PCs, for Σ and <F T >. PCs, indicating amplitude of each EOF as it varies through time, are inset; percent total variance explained by each mode is indicated beneath EOFs. Notice color bars of standardized EOF amplitudes differ for Σ and <F T >.

10 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 10 EOF accounts for ~40% of the total variance in that region. However, the third modes of each parameter do capture the gyre center with higher amplitude structure. They also add further refinement to the northern rim areas, but clearly the different PC variability suggests that the third EOF structure is adding more temporal stability to the short wavelength interannually-varying structure in the northern rim. Examination of the temporal variability (PC) of the modal amplitudes shows that mode 1 is highly periodic, dominated by a narrow band 5-year cycle, whereas modes 2 and 3 are dominated by longer period trends persisting for approximately 10 years; e.g., Σ mode 2 decreases from ; mode 3 from For convenience, we will refer to these modes as showing decadal scale variability, recognizing that the series are too short to clearly define the time scale formally as such Circumpolar Teleconnections. Now consider how the temporal variability of the Weddell modes covary with circumpolar SIE *. To evaluate this we correlated the detrended leading (3) PCs of Σ and <F T > to SIE * (of YM00) spanning the circum- Antarctic at 12 longitude non-overlapping windows. Correlations were computed over a broad range of lead/lag relationships, but because the bulk property parameters are integrated properties and sample cross correlation functions (ccf) have considerable smearing of the lags relative to the true ccf, lags 12 months are probably indistinguishable from those of 0 lag. Consequently, we only present lags of maximum correlations when they exceed 12 months, or there is some other reason to assume them meaningful. As exemplified by Figure 5, PC-SIE * correlations were typically strong in the Pacific sector and Weddell gyre region (e.g., r max = and 0.81 for PC2 of Σ and <F T >, respectively in the western Weddell, with similar maximum r-values occurring for the other PCs and in the Pacific basins as well). At longer lead/lag times, a strong correlation is typically realized in the Indian Ocean center. These spatial patterns, as well as their space/time (lag) distribution reflect the geographic concentrations of coherent signal presented in Figure 4 of YM00 when correlating SIE * to various extrapolar indices. However, here the patterns do not show the eastward propagation of r max with lag, consistent with an apparently propagating SIE * anomaly field as expected with the Antarctic Circumpolar Wave of White and Peterson [1996]. Rather, we find a predominantly static or restricted eastward migration of anomalies. We do see strong evidence and clear delineation of the Antarctic Dipole of YM00. That feature is manifested by SIE * in the Amundsen/Bellingshausen Seas being strongly anticorrelated to SIE * of the western Weddell gyre region; the eastern Weddell, Drake Passage and Ross Sea regions are in-phase nodes enveloping the dipole something clearly apparent in the correlation patterns here. Figure 5. PC1 of Σ and <F T > superimposed on SIE * from Amundsen/Bellingshausen region to show nature of strong correlation (r Σ =0.74; r <FT > =0.61). The Antarctic Dipole signal is strongest in the PC2- SIE * correlations: there is a systematic change in the sign of r when moving eastward and crossing the boundary between the eastern Ross Sea and Western Amundsen Sea (at ~120 W), another sign change when crossing from the Bellingshausen Sea into the Western Antarctic Peninsula region (at ~70 W), and finally another sign change near the Greenwich Meridian, separating the eastern extension of the Weddell gyre (where the Circumpolar Deep Waters appear to enter the subpolar gyre) from the western portion. PC1 shows the clear delineation of the Amundsen/Bellingshausen and western Weddell, but not as systematically, and the broader coherent relationships with Ross Sea and eastern Weddell are not quite as clear as for PC Extrapolar Teleconnections. To evaluate the relationship of the Weddell OAI system modes to extrapolar climate, we examine correlations between PCs and global gridded SAT * and the 4 climate indices described in Section 2. The correlation results reflect many of the teleconnections of YM00 for their case of extrapolar climate correlations involving SIE * in the Antarctic dipole region. Specifically, the strongest correlations for all PCs (see Figure 6) typically involve the ENSO region of influence, including the Pacific, Indonesia, western China, the tropical belt of the Indian Ocean/Africa. Like

11 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 11 Figure 6. Correlation maps where colors reveal magnitude of correlation (r) between PCs 1-3 (a-c) for _ and time series of detrended near surface temperature anomalies (SAT * ) around the globe. Sample PDF for correlation map is compared to bootstrap PDF for each mode, to assess overall significance of correlations achieved. Significance of individual correlations are indicated by contours showing integer number of standard deviations from mean correlation value expected from bootstrap PDF generated for every global grid cell of SAT *. Significance accounts for autocorrelations in space, time and multiplicity (see Appendix for discussion of significance).

12 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 12 YM00 we also find strong links to the Hudson Bay region, and regions near and/or encompassing southern South America, Africa and New Zealand. However, in the present case, the modes seem to show more consistent extrapolar regional foci than in YM00. Also, we find distinct patterns associated with each OAI mode, perhaps suggesting that each mode is linked to different extrapolar climate characteristics or represents a different mechanistic link. For all 3 modes the correlations peak at r > 0.8. As above, lags are only stated when exceeding 12 months, or there is some other reason to assume them meaningful. Statistical assessment of the correlation maps are presented in Figure 6 via confidence interval contours, whose derivation are described in Appendix 1. The significance of the correlations are determined from the probability mass functions (called PDFs here though recognizing and treating them as mass, not density, functions) inset in Figure 6. The "sample" PDF for each correlation map is presented as a histogram and it reflects the distribution of r-values achieved in the PC versus SAT * correlations presented by color-coding on the corresponding map of Figure 6. The more continuous-looking "bootstrap" PDF is generated using bootstrap techniques (see Appendix for discussion). It represents the distribution of r-values realized when generating 1000 correlation maps between SAT * and colored noise instead of PCs. Conservatively, the colored-noise has the same spectral coloring (i.e., lower order statistical moments, autocovariance and quasiperiodicity) as the PCs used in the sample correlation. Mode 1. This gravest mode appears to be a "global" mode, showing considerable (significant) covariability about the globe. Inspection of the correlation map (Figure 6a) reveals several interesting patterns of note. Foremost, the mode strongly captures the Antarctic Dipole of YM00, as well as its extension into the tropical Pacific and Atlantic. Specifically, the Amundsen Sea pole is in-phase with central tropical Pacific variability and the Weddell pole, of opposite sign to the Pacific pole, is in-phase with eastern tropical Atlantic variability. Meridional banding throughout the Atlantic from poleto-pole, noted in YM00, is also captured particularly well by this mode, even in the highest northern extent. This suggests that one might expect to see good correlation between mode 1 and the NAO, but as discussed later, this correlation is not particularly strong. Finally there is strong covariability with the entire Western Pacific- Indonesian corridor, as well as strong regional links with each of the continents. The entire Pacific correlation pattern is reminiscent of the decadal ENSO signal region of influence, while the tropical Atlantic pattern is similar to that of the Tropical Atlantic Variability (TAV) region of influence, centered predominantly on the south equatorial branch of the TAV. Statistically, this mode shows a significant positive shift in the mean r-value of the correlation map relative to that expected from the bootstrap PDF, as shown in the Figure 6a inset. However, the number of large r-values achieved globally (those in the upper 2.5% level of significance) are only 0.5σ more than to be expected from random chance involving colored-noise. We believe this reduced significance at highest r-values is a reflection of the strong periodicity inherent in this mode (nearly a perfect 5 year cycle). Thus, for noise with this dominant frequency band admitted (a conservative estimate), the noise's random phase implies that most of the random correlations will be of small correlation (thus not really altering the central body of the bootstrap PDF), but when the random phase of the narrow-band noise series is coincidentally similar to that of the climate variable (SAT * ), the alignment of the large variance frequency component will ensure a higher than otherwise expected r-value. This increases the relative frequency of occurrence of the highest r-values in the tails in the bootstrap PDF, tending to minimize the rarity of large r- values in the bootstrap correlations (and thus diminish the specific significance of the large r-value correlations achieved in the sample). Regardless, the significance at individual global gird cells (accounting for autocorrelation in space and time, and multiplicity) still show surprisingly widespread statistically-significant teleconnections. Mode 2. The second mode appears to be more clearly an ENSO related mode, though it too shows global (significant) teleconnections (Figure 6b). In fact, this mode actually shows much of the same global distribution as mode 1, though here the teleconnections are of opposite sign than that of mode 1. Also for this mode the Pacific ENSO pattern is more significant and there is more concentration over the oceans, than in modes 1 and 3, which show more links to continental regions. The Antarctic Dipole is not as obvious in this mode and its Pacific branch, linking the Southern Ocean to the central Pacific is shifted westward to the Ross Sea. The Atlantic branch, linking the Southern Ocean to central Atlantic is tied more strongly to the northern cell of the TAV pattern. It is interesting to note the similarity in patterns between modes 1 and 2 given the considerable difference in the dominant time scales of variability between PC1 and PC2, the former showing a strong interannual cycle and the latter more "decadal" variability. This not unlike the earlier findings of Zhang et al. [1997] who showed that when separating ENSO into its long (interdecadal) and short (interannual) time scales, the two components more or less respond at these unique time scales with similar regional patterns. Here

13 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 13 too we seem to show a similar spatial distribution of teleconnections despite opposite signs and different time scales. Statistically, the sample PDF for this mode shows a significant shift of the mean r-value toward more positive values, though this shift is more due to an extension of the high r-value tail of the sample PDF relative to that of the bootstrap PDF. Of the highest r- values (in the highest 2.5% of the PDF), the sample correlation map is ~3σ above those achieved through the 1000 bootstrap colored-noise correlation maps. Thus this mode seems to show a more overall teleconnection significance (i.e., overcoming problems of multiplicity) than mode 1. Mode 3. Mode 3 shows (Figure 6c) elements of each of the two graver modes, though covariability with the Atlantic seems to dominate, with the Indian Ocean and Mesopotamia showing strong links as well. There are still clear signs of the ENSO Pacific pattern, but the significance is lowest in this mode relative to the other two modes, except in the western tropical Pacific where the correlation is high and the significance strong. This mode displays no indication of the Antarctic Dipole, but curiously shows a strong positive correlation to both pole regions of the Dipole Statistically this mode shows the strongest and most significant nonzero mean correlation for the correlation map, even though visually the teleconnection pattern does not seem to be as broad as for the other two modes. The highest r-values occur in the upper 2σ range relative to the bootstrap PDF, and the overall most significant link is achieved with this mode and the Hudson Bay area of North America (r > 0.8, confident at > 2σ). Climate Indices. We also investigate the relationship between the Weddell upper ocean characteristics and extrapolar climate variability as measured by the climate indices: NINO3, NAO, SOI and NPI (for PNA). Correlations significant at better than the 95% confidence limit include: (1) mode 1 does not show any particularly strong relationship (in term of explained variance) to any of these four, but achieves r = with NPI and 0.51 with SOI; (2) mode 2 shows strong correlations with SOI (r = -0.7); and (3) mode 3 strongly covaries with NINO3 (r = -0.73) and with SOI (r = 0.64). While these show high significance, none show an overwhelming amount of shared variance, nor do they show stronger links than realized with the regional distributions of SAT *. Therefore, we focus our discussion and interpretation primarily on the global SAT * teleconnections in Section 5, below. 4.2 Super-Data (Non-Interpolated) Analysis Having found widespread statistically-significant teleconnections between the OAI variability in the Weddell gyre region to extrapolar climate, we now investigate whether these correlations are an artifact of the OA interpolation. We do this by repeating some of the ENSO-related correlations using the (noninterpolated) super-data, instead of the gridded data. Motivated by the original results of Figure 1, the results of correlating NINO3 to the super-data as well as the OA gridded data are presented in Figure 7. Here correlation significance is not particularly relevant since we are more interested in examining the influence of the interpolation on the patterns and degree of correlations, hence we only focus on the nature of the relationship between super-data and gridded results. The results are interesting from two perspectives. (1) The correlation patterns of Figure 7, are quite similar to the spatial pattern of EOF1, suggesting that the interpolation has not distorted the spatial patterns, other than its introduction of enhanced coherent structure in the SW region of the Weddell as previously noted. (2) The correlation patterns are similar for both the superdata and interpolated data suggesting that the OA interpolant has not introduced spurious coherent structure into the gridded data set. Furthermore, but perhaps more noteworthy, is that the correlations actually achieve higher r-values using the super-data than the gridded data. Examination of the correlated time series suggests that the reason for this is the filtering introduced by the reduced-space OA interpolant. That is, the interpolated series capture the broadest features, but the filtering has eliminated the subtle nuances present in each ENSO event. These are preserved in the super-data however, resulting in a higher degree of correlation (suggesting that the space reduction eliminated more ENSO-related signal variance than noise). Regardless, the preservation of the high degree of correlation with ENSO lends support to the fact that the gridded data present a reasonable approximation to missing values, and that the correlation results are not a methodological artifact. Similar results are achieved when comparing the correlation of specific SAT * grid locations to the Weddell super-data and gridded data. 4.3 Local/Regional Physical Controls on Bulk Parameter Variability In an attempt to identify plausible mechanistic links between the extrapolar variability and the Weddell OAI, we now wish to investigate what changes in the physical characteristics of the upper ocean water column are dominating the variability in the modes of Σ and <F T >.

14 MARTINSON AND IANNUZZI: WEDDELL GYRE AND GLOBAL CLIMATE 14 Figure 7. Correlation maps of NINO3 to Weddell gyre bulk stability using: (a) super-data (uninterpolated) and (b) OA interpolated data, with showing r for each grid cell. Both of these OAI parameters are functions of SD w and and <F TB w. <F T > has an additional dependency on T T >. Interestingly, despite the different through characteristic time scales of the different OAI modes, all the pycnocline. SD w, TB w and T are dependent upon 3 show a similar dominance of external parameter the external system parameters: S ml, z ml, T pp, S pp, z pp (T ml variability, though the relationships are considerably is essentially invariant since its winter-average value is stronger and distinct for Σ relative to those for <F T >. assumed fixed at the freezing point, so it is not The overwhelming majority of change is attributed considered here). Consequently, we wish to determine to changes in TB w (r 2 = 98%, 94% and 96% for PC1, which of the external system (gyre-characteristic) PC2 and PC3, respectively) and to a lesser extent by SD w parameters are dominating the bulk parameter variations (r 2 = 32%, 1% and 26% for PC1, PC2 and PC3, and what mechanisms are consistent with those changes. respectively). Note that the ascribed variance of TB w and To investigate this dependence, we apply the OA on SD w exceeds 100% of the variance, but this simply the 5 external system parameters and correlate the PCs of reflects covariability between TB w and SD w. The each of their gravest 3 modes to the dominant PCs of Σ predominant control on SD w (90% of the variance) is due